Focusing and guiding X-rays with tapered capillaries

ABSTRACT

Apparatus for directing and focusing X-rays by the new method of confinement is disclosed. A capillary having an inlet end and an outlet end with a generally tubular or rectangular inner wall surface defines a longitudinal central opening. The central opening is tapered inwardly from the inlet end to the outlet end. X-rays are directed into the inlet end at angles less than the critical glancing angle for the inner wall surface to direct X-rays through the capillary to a focus point near the capillary outlet end.

This application is a continuation of application Ser. No. 261,146,filed Oct. 24, 1988.

FIELD OF THE INVENTION

The present invention relates to a method and apparatus for focusing andguiding x-rays. More particularly, the invention is directed to the useof tapered capillaries having an inlet end on which x-rays are incident,the x-rays striking the inner surface of the capillary below thecritical glancing angle and reflecting from the inner surface due tototal external reflection. The capillary is tapered inwardly towards theoutlet end so that the x-rays are focused in a broad band of energies.Greater focusing is possible with softer x-rays and from undulatorsources.

BACKGROUND OF THE INVENTION

For many uses of x-rays, it is necessary or desirable to focus them intoa small spatial region. The standard methods require very precisedimensions in the focusing elements, of the order of microns or less,and as a consequence such methods are difficult to achieve andexpensive. The present invention is directed to a novel method andapparatus for focusing x-rays where the need for extreme precision isobviated, and as a result is cheaper and easier to fabricate. Theapparatus also has a high efficiency of transmission.

The present invention is an extension of the recent progress that hasbeen made in forming subwavelength beams of light with finely taperedglass capillaries. The use of untapered capillaries as light pipes forx-rays without focusing has previously been described in the art;however, the feasibility of using tapered capillaries to focus x-rayshas not been reported.

SUMMARY OF THE INVENTION

The present invention is directed to a method and apparatus for focusingx-rays over a broad band of energies to dimensions of less than 0.1microns, the exact dimension depending on the energy of the x-rays andthe initial collimation of the x-rays before they enter the capillary.The method and apparatus may also be used for containing x-rays within adefined enclosure. Briefly, the invention provides a tapered capillarywhich may take several forms, the simplest of which is a small diameterglass tube which tapers linearly inwardly from an input end to an outletend. The rate of taper is constant and, for a glass tube, the innersurface is totally reflective for x-rays striking that surface below thecritical glancing angle. A more preferred form of the invention is astepped capillary wherein the inner surface tapers in a series of steps,each having a different angle of linear taper so that for the firstlength of the tube, the inner surface has a first linear taper, for thenext adjacent length, the inner surface has a second, steeper angle oftaper, and so on for each adjacent length of the tube. The mostpreferred form of the invention incorporates a very large number ofsteps each having an increased degree of taper. The larger the number ofsteps, the more closely the shape of the inner surface of the capillaryapproaches an elliptical shape, which would be the most preferred formof the invention.

the capillary is internally reflective of x-rays which strike the mirrorwall surface at less than the critical glancing angle so that x-rayswhich enter the inlet of the capillary at below this critical angle willbe substantially completely reflected along the length of the capillary.Although there will be some loss of intensity due to reflection losses,thereby restricting the number of reflections that can be permitted asthe x-ray travels through the capillary, these losses can be minimizedby controlling the amount of taper. The advantage of such a taper,however, is that a focused beam is produced which provides a higherx-ray intensity in a smaller area at the outlet of the capillary.

The device of the present invention permits x-rays to be accuratelydirected so that they can be transmitted, diffracted, refracted,scattered, reflected or absorbed with a spatial resolution of betweenless than 0.1 micron and 100 microns, which resolution is characteristicof microprobe applications. The capillary also can serve to extend anx-ray source from its origin to another point in space in a way which isan analogous to the way an optical fiber transmits light. This allowsthe device to be used in, for example, medical applications that requirefocused x-ray spots without irradiating intervening tissue.

The device of the present invention maintains the polarization of thex-rays as they pass through the capillary, including linearly andcircularly polarized x-rays.

The capillary provides a very fine focus point for the x-rays, enablingthe capillary to function as an x-ray microscope for imaging, and toperform x-ray diffraction, x-ray absorption, x-ray tomography, x-rayfluorescence and x-ray absorption fine structure analysis with highspatial and time resolutions. The device can also be used as an x-rayamplifier and/or laser by incorporating media within the capillary thatcan be excited to produce x-ray emissions. The device can also be usedas a source for non-linear excitation of transitions, and to investigateprocesses while they are rapidly evolving.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and additional objects, features and advantages of thepresent invention will become apparent to those of skill in the art froma consideration of the following detailed description of preferredembodiments thereof, taken in conjunction with the accompanyingdrawings, in which:

FIG. 1 is a diagrammmatic illustration of a linearly tapered capillarywherein the angle of divergence of the beam is represented by α and theangle of taper with respect to the horizontal is represented by theangle β;

FIG. 2 is a diagrammatic illustration of an experimental layout formeasuring x-ray intensities of beams transmitted through a capillary;

FIG. 3 is a diagrammatic illustration of a step-tapered capillary;

FIG. 4 is a diagrammatic illustration of an improved step-taperedcapillary;

FIG. 5 illustrates in schematic form an experimental arrangement fortesting the present invention;

FIG. 6 illustrates in steps a. through g. the focusing capability of thedevice of the present invention at different distances from the outletof the capillary, and

FIG. 7 illustrates a capillary constructed to taper in only onedimension, in accordance with the present invention.

DSESCRIPTION OF PREFERRED EMBODIMENTS

FIG. 1 illustrates in diagrammatic form a tapered capillary 10 formed bya continuous glass wall 12 having an interior surface 14 and an exteriorsurface 16. The capillary has an inlet end generally indicated at 18 andan outlet end generally indicated at 20. As illustrated, the interiorsurface of the side wall 14 has a continuous, inward, linear taper fromthe inlet end 18 to the outlet end 20. The dimension of the capillary atthe inlet end is indicated at Y_(O), while the dimension at the outletend is indicated at Y₄, with the dimension decreasing continuously fromY_(O) to Y₄. The capillary may be tubular as illustrated in FIG. 1, inwhich case the dimensions Y_(O) and Y₄ are its inner diameter, or it maybe rectangular, in which case these dimensions are the height of thecapillary inner passageway.

An experimental capillary assembly is illustrated diagrammatically inFIG. 2, wherein X-rays, indicated by the arrows 30, are emitted by asource 32, are directed through an aperture or window 34, and through apinhole aperture 36 to effectively collimate the x-rays for entry intothe capillary 10. X-rays entering the capillary follow various paths,depending upon their angle of approach, but typically follow a path suchas that indicated by the dashed line 40 in FIG. 1. X-rays striking theinner surface of the capillary at an angle less than the criticalglancing area will be reflected from the surface rather than enteringthe glass wall 12. Below this critical angle, any intensity loss uponreflection from surface 14 will be small, for the x-ray is almostcompletely reflected. The intensity profile of the beam at the outletend is determined by measuring the signal in detector 50 as a functionof the position of a polished edge stop 52.

In FIG. 1, the line 42 is parallel to the longitudinal axis 44 of thecapillary and an incident x-ray enters the inlet at 18 at an angle αwith the axis. By geometry it can be shown that after the firstreflection at an inner capillary dimension Y_(O) the next reflectionwill occur at an inner diameter Y₁ as indicated by the dotted line 40.The relationship of these two diameters is expressed as follows:

    y.sub.1 /y.sub.O =sin [α+β]/sin [α+3β]Eq. 1

The incident ray 40 will again be reflected from the surface 14 atdiameter Y₁ and another cycle of reflections will take place. In thiscycle, the ray is considered to be incident at the diameter Y₁, with thenext reflection occurring at Y₂. The relationship between diameters Y₁and Y₂ is given by:

    y.sub.2 /y.sub.1 =sin[α+3β/sin [α+5 β]Eq. 2

Multiplying equations 1 and 2 together, one obtains:

    y.sub.2 /y.sub.O =sin[α+β]/sin [α+5β]Eq. 3

By induction it is easily seen that in general:

    y.sub.n /y.sub.O =sin [α+β]/sin [α+(2n +1)β]Eq. 4

where Y_(n) is the diameter of the capillary at the (N-1) th reflection,and

    [α+(2n=1) β]                                    Eq. 5

is the glancing angle at that reflection. In order to remain in thetotal reflection region the following is required:

    α+(2n+1) β≦θc                      Eq. 6

Since generally the critical angle for x-rays satisfies the requirementthat θc be much less than 1, we can approximate equation (4) as follows:

    m.sub.n 5 y.sub.n /y.sub.O ≈(α+β)/ [α+(2n +1) β]                                                   Eq. 7

or by the following approximation:

    y.sub.n [α+(2n+1) β]=constant.                  Eq. 8

In all of the foregoing equations, the angle β is the angle of the innersurface 14 with respect to the longitudinal axis of the capillary, andthis angle represents the amount of taper in the capillary. The maximumdemagnification m_(m) (the minimum value of Y_(m) /Y_(O)) for a givenangle β is given by the following relationship:

    m.sub.m =(α+β)/θ.sub.c                    Eq. 9

As an example of this demagnification consider the bending magnetradiation where the source 32 of x-rays is a synchroton, and whether αis approximately 0.5 ×10⁻⁴ radians. With such an arrangement, themaximum demagnification as the angle approaches zero would be 1/80,since critical glancing angle θc for glass is approximately 4×10⁻³radians.

Although theory indicates that losses for x-rays below the criticalglancing angle are negligible, experimental results show that in factthey are larger than the ideal calculated values. Therefore, the optimumdesign for synchroton radiation will have to be one that does notinclude a large number of reflections. From the demagnification equation(9) it is apparent that for a perfectly parallel incident beam, whereα=0, an arbitrarily small spot size can be achieved simply by making thetaper of the capillary very small so that the angle β approaches zero.This in turn requires having a large number of reflections, but sincereflections cause losses, this is to be avoided if possible. Conversely,if the number of reflections is to be reduced, β has to be increased,and this increases the final spot size that can be achieved by a facotrof (α+β)/ α. Accordingly to get the maximum intensity from a lineartapered capillary, there has to be a compromise between the taper andthe number of reflections in order to get the smallest spot size withmaximum put through. As indicated above, the intensity profile of thex-rays passing through the capillary may be measured by monitoring thesignal in a target such as a detector 50 as a function of the positionof the polished straight edge 52 of an x-ray absorbing material (seeFIG. 2).

Improved results are obtained in the embodiment illustrated in FIG. 3,to which reference is now made. As illustrated, the capillary 60includes a glass side wall 61 which includes stepped wall segments 62,64 and 66, for example (a fourth segment is not shown). Each segment hasan X-ray receiving, or inlet, end and an X-ray emitting, or outlet, end,with the outlet of each segment being connected to the receiving end ofthe next succeeding segment. The wall segments include correspondinginner wall surfaces 68, 70 and 72, respectively, each of which forms adifferent, and increasing, angle with respect to the longitudinal axis74 of the capillary. Thus, for example, the inner wall surface 68 formsan angle β_(O) with the axis, the wall section 70 forms an angle 3β_(O), and wall surface 72 forms an angle 9 β_(O) as illustrated in FIG.3.

As illustrated in FIG. 2, the source 32 produces numerous X-rays, butonly those which pass through apertures 34 and 36 will be incident onthe inlet end of the capillary. Some rays will enter the capillary nearits axis, while others will enter the extreme edges of the inlet. Thepath 76 in FIG. 3 represents the path of an extreme X-ray and enters thecapillary at, for example, an angle α which is less than the criticalglancing angle. After a single reflection in a first linear taperdefined by wall surface 68, the angle of the reflected x-ray beam withrespect to the axis 74 will be increased, or enhanced, with the increasebeing from α to α+2β. This increases the incident angle the x-ray makeswith the surface of the first linear taper from (α+β) to (α+3β). Thisresults in a demagnification ##EQU1##

Each further reflection of the beam within the capillary will result inan increased incident angle, resulting in a corresponding decreasingdemagnification per reflection. This is corrected for by increasing thetaper β along the capillary to match the new angle of incidence for eachreflection, as illustrated in FIG. 3. In capillary 60, a step isprovided at the point where the x-ray following path 76 makes its nextreflection; this is, herefore, the junction 78 between segments 62 and64 and corresponding wall surfaces 68 and 70. The path 76 represents theextreme reflection which occurs only once in each tapered portion;x-rays at smaller angles will have a smaller number of reflections inthe segments.

For the stepped taper illustrated in FIG. 3, each segment receiving endis one half the diameter of the receiving end of the preceding segment;that is, the diameter at junction 78 is 1/2 the diameter at the inletend 80 of the capillary. Similarly, the diameter at the junction 82between the wall surface 70 and the wall surface 72 is 1/2 the diameterof the capillary at junction 78. Furthermore, the angle of incidence ofthe ray for each step relative to the axis of the capillary will bethree times the angle in the previous step.

In the embodiment of FIG. 3, if α=0.5×10⁻⁴ radians, the taper for theinitial surface 68 is set to β₀ =0.5 ×10⁻⁴ radians. The subsequenttapers are as follows:

    β.sub.1 =1.5×10.sup.-4 radians

    β.sub.2 =4.5×10.sup.-4 radians

    β.sub.3 =13.5×10.sup.-4 radians

For these sections of taper, the total demagnification m_(m) =(1/2)⁴=1/16, while the glancing angle of incidence at the last reflection atthe junction 82 is 27×10⁴ radians, still below the critical angle.Assuming no losses on reflection, this gives an intensity enhancementfactor of 16², or 256. A more realistic number as indicated bymeasurement of experimental capillaries is a 6% loss per reflection.This loss in relection adds a factor of 0.78, giving a total intensityenhancement per unit area of 200 at the output of the tapered capillary.This may be compared with the linear taper of FIG. 1 with the samedemagnification factor, in which a loss in reflection factor of 0.50 isobtained for the 11 required reflections along the length of capillary,giving a total intensity enhancement per unit area of only 130.

Still further improvement is illustrated in FIG. 4, wherein a capillary100 incorporates sidewall segments 102, 104, and 106, (a fourth segmentis not shown) joined together at junctions 110 and 112. The wallsegments have interior surfaces 116, 118, and 120, respectively, whichare joined together with the emitting end of one segments joining thereceiving end of the next segment at the junctions 110 and 112. Thecapillary has an inlet end 124 and an outlet end 126, with alongitudinal axis 128.

In the embodiment of FIG. 3, the initial taper intersects the extremeray represented by dotted line 76 only once. The limitingdemagnification factor can be improved, in accordance with theembodiment of FIG. 4, with no increase in the number of reflections, ifthe step between adjacent segments of the wall is started sooner thanthe location where the extreme ray would make its next intersection ifthe taper were the same length as that of FIG. 3. Thus, the taper isstepped at junction 110 and the extreme ray represented by dotted line130 does not strike the wall of the capillary until the region indicatedby the line of intersection at 132 on surface 118. The ray 130 thenstrikes a wall section having a smaller diameter than was the case inthe embodiment of FIG. 3, with a resulting greater demagnification,which is a positive gain for the purpose of the present invention. Onthe other hand, rays with a smaller incident angle such as thoseindicated by the dotted line 134, which are closer to being parallel tothe capillary axis 128, will have their first reflection at the secondtapered section 118, and from equation 4 such a ray will have a smallerdemagnification. However, these rays at smaller incident angles areprecisely the rays that require less demagnification. An ideal designwould be one which matches these two requirements to make the final sizethe same for all rays.

A stepped approximation to this ideal is illustrated in FIG. 4 whereineach step occurs as xl_(i), where is equal to 0, 1, 2, 3, etc., wherel_(i) is the tapered length of each step of the capillary of FIG. 3, andwhere x is approximately 0.55. For capillary 100, and with fourreflections along the length of the capillary, the demagnificationfactor m_(m) for a ray is 91, with the same reflection loss factor of0.78. As a result, the total intensity enhancement per unit area on atarget at the end of the capillary is 6,400. This optimized taper has amiximum demagnification factor m_(m) that is larger than the value 80for the limiting linear taper. In fact, the taper in FIG. 4 is thebeginning of an approximation to the ideal focusing element in which thewall surfaces 116, 118 and 120 form an ellipse. A device such as thatillustrated in FIG. 4 would operate with an x-ray source of an electronbunch from a synchrotron radiation ring which would typically be 0.1 mmin diameter. A part of an elliptically shaped surface of rotationtheoretically could focus by imaging a spot of 10 μm diameter from asource of 0.1 mm. However, such a focusing element would require extremedimensional precision. Such precision is not necessary for the taperedstepped capillary illustrated in FIG. 4, which does not image, butfocuses by guiding within the capillary. The following table sets forthexemplary parameters for the construction of tapered capillaries inaccordance with FIGS. 3 and 4:

                  TABLE I    ______________________________________    FIG. 3             Taper    βo                                     3 βo                                          9 βo                                               27 βo    STEP-TAPER         Length   5.00 0.832                                          0.139                                               0.0230    (βo = 0.5 × 10 - 4)                       (meters)    FIG. 4             Taper    βo                                     3 βo                                          9 βo                                               27 βo    STEP-TAPER         Length   2.75 1.76 0.164                                               0.0172    (βo = 0.5 × 10 - 4)                       (meters)    ______________________________________

As explained above, the advantages of capillary focusing are itsinexpensive cost, simplicity of fabrication compared to other methods,high throughput, and broad bandpass characteristics. Its inexpensivecost and simplicity of fabrication are related to the fact that it doesnot require the extreme precision of dimension or shape that isnecessary in other currently available methods such as mirrors and zoneplates. For example, in mirrors and zone plates, and inaccuracy whichcauses a deviation of the x-ray wave front will ruin the focus sincesuch devices are placed relatively far away from the focal point; thatis, on the order magnitude of meters or centimeters. On the other hand,in the present invention such accuracy is not required, since the sampleto be irradiated can be placed a fraction of a millimeter from thecapillary output. Thus, any variation in shape or non-specularscattering will still confine the x-rays within the capillary and aslong as they exit from the tip, they will still contribute to the focus.

The maximum focus possible by the capillary is limited by the criticalangle θ_(c), as explained in equation 9. Thus, m_(m) can be increased ifα, which is the divergence of an x-ray beam from the axis of thecapillary, is made smaller so that β can be decreased. Typically onedesires to have β approximately equal to α. The insertion of devices insynchrotron radiation rings, such as undulators, give outputs withsmaller values of α than are obtained from bending magnets. Therefore,with such devices and with the present technique, very small focusedx-ray spots can be achieved. An alternate way to increase m_(m) is toincrease θc. The expression of θ_(c) is given by:

    θ.sub.c =(4πne.sup.2 /m).sup.1/2 /ω         Eq. 11

where n is the effective electron density per unit volume, ω is theangular frequency of the x-rays, and e and m are the electron charge andmass respectively. From equation 11 it is seen that there are two waysincrease θc. One is to increase n and the other is to increase ω. Thedependence on n goes as the square root and the improvement by changingthe material on the inner surface of the capillary is limited topractice, to a factor of 2.5. However, the dependence of ω is inverseand an order to magnitude increase in m_(m) is possible by using softerx-rays.

In an experimental test of the invention, a conventional fixed anodex-ray source was used. Such a source does not have the collimationinherent in synchrotron x-ray radiation. However, the effectiveness ofthe present method was demostrated with such a source. For thisnon-collimated beam using a constant bore capillary; i.e., a capillarywithout a taper, focusing occurs because of the increase of theeffective solid angle at the output of the capillary compared to apinhole of the same diameter located at the caillary output. If nolosses are assumed in the reflectivity, the increase in intensity isgiven by the ratio of the solid angle subtended by θ_(c) to thatsubtended by the capillary exit. For these measurements, a glasscapillary having a constant bore of 0.88 mm, where β approached zero,with a length of 64 cm was used. For this capillary, the critical anglewas calculated to be 4×10⁻³ radians for Cuα radiation and therelectivity at this angle was calculated to be 97.5%. Althoughmeasurements on a constant bore glass tube have previously beenreported, those measurements were made on tubes having larger diameterswhich were composed of six sections mechanically aligned to one another.The connection between sections introduced some discontinuities whoseeffects, though small, were uncertain.

The experimental arrangement is schematically illustrated in FIG. 5,wherein the x-ray source 232 is a 1 mm by 1 mm point focus of a Cutraget Philips x-ray tube, operated on a Philips PW 1300 x-ray generatorat 20 KeV and 4 mA. In this experimental arrangement, all rays thatenter the capillary 210 at incident angles below the critical angleshould be transmitted through the tube through the outlet end. Formeasurement of the capillary throughput, a pinhole 236 which was 0.1 mmin diameter was placed at a distance of 130 mm, plus or minus 3 mm fromthe center of the x-ray tube, with the pinhole emitting an x-ray beam ofangular width of approximately 1.1/130=8.5×10³¹ 3 radians which isslightly more (by 5%) than the angular acceptance of the glasscapillary, this angular acceptance being twice the critical angle. Aconstant bore capillary 210 was placed on a groove in an aluminum tray,which in turn rested on two jacks and microslides, permitting finepositioning of the device in both directions perpendicular to the beamand independently at each end of the capillary. The entrance tip of thecapillary touched the pinhole. The scintillation counter was positionedat distance of 5 cm from the exit tip. Four nickel foils were placed infront of the counter window, decreasing the incident Cu k intensity byabout 80% and enhancing the monochromaticity of the beam.

Measurements were conducted by first removing the capillary, maintainingthe pinhole at its same position and observing the x-ray intensity I_(o)at the counter which subtended a large enough solid angle to detect allof the radiation that passed through the pinhole (pinhole to counterdistance 69 cm). It was noted that the intensity I_(o) remained constantto within 3% on moving the pinhole about 3 mm in each of the twoperpendicular directions to the beam.

Subsequently, the capillary was replaced between the pinhole and thecounter and after some adjustment of its alignment an x-ray intensitywas observed to pass through the capillary as evidenced by the countingrate of the scintillation counter rate I_(c) was reached and measured.The capillary was then removed again and the counting rate I_(o) wasredetermined, resulting in the same value as the first measurement.

Both the values for Io and Ic were measured four times for 100 secseach, giving an accuracy in counting statistics better than 0.1%. Theobserved rates are I_(o) =10155 plus or minus 5 counts/sec and I_(c)=7880 plus or minus 5 counts/sec. Since both I_(o) and I_(c) weremeasured under the same absorption length in air they can be compareddirectly. Considering the fact that 95% of the incident intensity hitsthe capillary below the critical angle and on the average a ray shouldbe reflected between 2 to 3 times based on the length and cross-sectionof the capillary, the theoretical ratio between I_(c) /I_(o) should be0.84 assuming 0.975 for the reflectivity. The actual values of I_(c)/I_(o) about give a ratio of 0.76 plus or minus 0.01 which is smallerthan the theoretical value, as expected.

The difference between the theory and experiment is a result ofdeviations in the experimental situation from the ideal. Thesedeviations are due to roughness of the capillary surface and imperfectalignment which includes slight bending of the capillary and undulationsthrough its length. The intensity enhancement at the exit of thecapillary as compared to the intensity from a pinhole placed at the sameposition as the capillary exit was a factor of (2θc)² ×(0.088/64)²×(0.78/0.9) =29! The factor 0.88/0.64 is the angle subtended by the exitdiameter at the pinhole, which is a distance of 64 cm. The factor0.78/0.9 is a result of the losses within the capillary and the 2 θc isthe angle subtended by the rays that totally reflect within thecapillary.

Exposures taken at distances of 0, 5, 10, 15, 20, 25 and 30 cm from theoutlet 220 of the capillary are indicated in FIG. 6 at points a-g. Asillustrated, the greatest degree of focusing occurred at about 5 cm,with the spot produced by the x-ray beam increasing gradually in sizewith distance from the exit. It was noted that the intensity at theoutput end was sensitive to the relative position of the pinhole and thecapillary. Thus, it has been demonstrated the x-rays can be focused andguided by a glass capillary.

In addition to the tubular or rectangular capillary which focuses in twodimensions by tapering in two dimensions, it is simpler to construct aone dimensional focusing element by tapering in one dimension. Such aone dimensional focusing element, which is diagrammatically illustratedin FIG. 7 at 260, can be bent into the desired tapers including the moreideal elliptical shape, greatly simplifying the construction of theelement. The inner surfaces 262 and 264 between the two plates 266 and268, respectively of flat and polished glass are bent in the more idealelliptical shape given by the equation ##EQU2## where x and y define avertical plane. The direction of the x-rays make only small angles tothe horizontal x-axis and they focus in the y-direction. The horizontalz direction is perpendicular to the x-y plane and there is no focusingin that direction. The slope from the horizontal of the inner surface atthe outlet is equal to the cirtical angle θc for total externalreflection of the x-rays, 270, which typically is 4×10⁻³ radians, andthe opening 272 at the outlet is 10 μm in the vertical direction. Theopening 274 at the inlet is 500 μm in the vertical direction. To producesuch an elliptical shape A² =5×10¹³ μm², B² =1.4×10⁵ μm², and the lengthl of the focusing element in the x-direction, the longitudinaldirection, is 1.8 m. This shape is suitable for an arrangement where thex-ray source 276 and the outlet 272 of the one dimensional focusingelement are approximately 15 m for one another.

Although the present invention has been disclosed in terms of preferredembodiments, variations and modifications may be made without departingfrom the true spirit and scope thereof as set forth in the followingclaims.

What is claimed is:
 1. Apparatus for directing and concentrating X-rayscomprising:a capillary having an open inlet end and outlet end andhaving an inner wall surface defining a longitudinal central opening,said capillary central opening being tapered inwardly in steps from saidinlet to said outlet end to gradually reduce the dimensions of thecapillary central opening, said inlet taper of each of said steps beinglinear, the angle of taper of each step being about three times theangle of taper of its immediately preceding step, the length of a firstof said steps at said input end being less than the length of the pathof travel of an X-ray beam within the capillary from its point of firstimpingement on said inner wall surface at an angle below a criticalglancing angle of said inner wall surface and a point of secondimpingement on said inner wall surface; and means directing X-rays intosaid capillary inlet at angles less than said critical glancing anglefor said inner wall surface, the linear taper of said central openingdirecting said X-rays through said capillary and concentrating all saidX-rays to exit at said capillary outlet end.
 2. The apparatus of claim1, wherein said inner wall surface is generally tubular.
 3. Theapparatus of claim 1, wherein said inner wall surface is rectangular incross-section.
 4. An elongated capillary for directing and concentratingX-rays, comprising:an open inlet at a first end of said capillary, saidopen end having a first cross-sectional dimension for receiving X-rays;an open outlet at a second end of said capillary, said outlet end havingsecond cross-sectional dimension defining an area of focus, said seconddimension being smaller than said first dimension; a continuous X-rayreflective inner wall surface defining a longitudinal central openingfor said capillary, said central opening having a longitudinal axis andsaid wall surface having an inward taper from said inlet end to saidoutlet end; and means directing X-rays of a first concentration intosaid capillary central opening throughout said inlet end at angles lessthan the critical glancing angle for the wall surface of said centralopening, the taper and reflective surface of said central opening walldirecting said X-rays through said capillary and progressively confiningsaid X-rays to provide at said outlet end a beam of a secondconcentration greater than said first concentration, said outlet beamhaving a cross-sectional dimension which is at least as small as thecross-sectional dimension of said outlet end.
 5. The capillary of claim4, wherein said opening is tapered in steps from said inlet end to saidoutlet end, each step comprising a capillary segment which is linearlyand continuously tapered and which has an X-ray receiving end and anX-ray emittingy end, with the emitting end of each segment having across-sectional dimension which is one-half the cross-sectionaldimension of the receiving end thereof, and wherein the taper of eachsegment has a taper angle three times the taper angle of the nextpreceding segment.
 6. The capillary of claim 5, wherein said meansdirecting X-rays into said capillary comprises a collimated synchrotronsource of X-rays.
 7. The capillary of claim 6, wherein said synchrotronsource is located to direct X-rays into said inlet end along said axis,the taper of the inner wall surface of each of said segments deflectingX-rays approaching said wall segments at said glancing angle or lessinwardly toward said axis to concentrate said X-rays at said outlet end.8. The capillary of claim 7, wherein said outlet end has a dimensionfrom about 10 microns to about 0.1 micron.
 9. The capillary of claim 8,wherein said inner wall surface taper for each segment directs saidX-rays to concentrate said X-rays without a common focal point.
 10. Amethod of concentrating X-rays to increase the intensity of an X-raybeam without point focusing the X-rays, comprising:directing a beam ofX-rays from a source into an open inlet end of a capillary having aninner surface defining a central through opening, said capillary openingto a capillary opening having an outlet end; tapering the inner surfaceof the central opening through the capillary inwardly to decrease thecross-sectional dimension of the capillary through opening from itsinlet end to its outlet end to thereby constrict the path of the X-raybeam; causing said beam of X-rays from said source to impinge on theinner surface of the capillary at angles below the critical angle oftotal external reflection of the inner surface so that the beam isreflected from the inner surface and travels through the capillary fromits inlet end to its outlet end, the constricted path reducing thecross-sectional dimension of the beam as the beam passes along thecapillary to thereby produce an output beam at the output of thecapillary having a higher intensity than the beam of X-rays directed tothe open input end of the capillary.--Rewrite claim 20 as follows: 11.The method of claim 10 wherein the step of tapering the inner surface ofsaid central opening includes forming the capillary in a series oftapered steps approximating an elliptical shape to thereby constrictsaid X-ray beam without producing a point focus.
 12. The method of claim11, wherein the step of causing the X-rays to enter the capillaryincludes directing X-rays to enter the entire cross-sectional area ofthe inlet end of said capillary at angles to impinge on variouslocations on said inner surface of said capillary.
 13. The method ofclaim 12, wherein at least some of said X-rays impinge on said innersurface a plurality of times in travelling through said capillary. 14.The method of claim 10, wherein the step of tapering the path of saidX-rays includes forming the capillary with a cross-section thatdecreases along the length of the capillary to provide an outlet openinghaving a dimension equivalent to the dimension of a focal point for theX-rays, the taper of the capillary inner surface constricting the beamdimension to the dimension of the outlet opening without focusing thebeam.
 15. The method of claim 10, wherein the step of tapering the pathof said X-rays includes forming the capillary with a pair of opposedsurfaces which are inwardly tapered to produce a cross-section thatdecreases in one dimension along the length of the capillary to providean outlet opening having one dimension equivalent to the dimension of afocal point for the X-rays, the taper of the capillary inner surfaceconstricting the beam in said one dimension without focusing the beam.16. The method of claim 10, wherein the step of tapering the path ofsaid X-rays inlcudes forming the capillary with a generally tubularinner surface which is generally tapered inwardly to produce across-section that decrease in two dimensions along the length of thecapillary to provide an outlet opening having its dimensions equivalentto the dimension of a focal point for the X-rays, the taper of thecapillary inner surface constricting the beam in two dimensions withoutfocusing the beam.